John says that when you compare two fractions with the same numerator you look at the denominators because the fraction with the greater denominator is greater is the correct explain and give an example
John is not correct.
Which is larger?
2 pieces of pizza cut into 4 pieces
Or
2 pieces of pizza cut into 10 pieces
Well, John is certainly on the right track. Comparing fractions with the same numerator does involve looking at the denominators, but let's put a humorous spin on it.
Imagine you're at a pizza party, and the pizzas are being cut into slices. Each person gets a fraction of a pizza. Now, let's say you and your friend John both get a slice with the same amount of toppings (numerator).
You notice that your slice has been cut into 8 pieces (denominator), while John's slice has been cut into 12 pieces. Naturally, you'd think that John got the bigger slice, right?
But hold on a second, here comes the Clown Bot with a funny twist! John's slice may have more pieces (denominator), but don't be fooled. Your slice, with fewer pieces (denominator), is actually bigger because each piece has more toppings. So in this case, your fraction is actually greater than John's!
So remember, when comparing fractions with the same numerator, the fraction with the smaller denominator is often greater. It's like a pizza party logic that pizza lovers can understand.
No, John's statement is incorrect. When comparing two fractions with the same numerator, you actually look at the denominators to determine which fraction is greater. However, the fraction with the smaller denominator is actually greater.
Here's an example:
Let's compare the fractions 1/5 and 1/3.
Since both fractions have the same numerator of 1, we look at the denominators. The fraction 1/5 has a smaller denominator compared to 1/3.
In this case, the fraction 1/5 is actually greater than 1/3 because the smaller the denominator, the greater the fraction.
John's explanation about comparing two fractions with the same numerator is partially correct, but it oversimplifies the process. When comparing fractions with the same numerator, the denominator does play a significant role, but it is not the sole factor in determining which fraction is greater.
To compare two fractions with the same numerator, you need to consider the denominators in relation to each other. Here's a step-by-step explanation:
1. Verify that the fractions have the same numerator. If not, you cannot directly compare them using this method.
2. Examine the denominators. The general rule is: the smaller the denominator, the larger the fraction.
3. If both denominators are the same (e.g., both fractions have a denominator of 5), they are equal.
4. If the first fraction has a larger denominator than the second fraction (e.g., 1/3 vs. 1/8), then the first fraction is smaller because the numerator is divided into smaller parts.
Example:
Let's compare 3/4 and 3/8.
1. The numerators are the same (3).
2. The denominator of the first fraction (4) is larger than the denominator of the second fraction (8).
3. Since the numerators are the same, because the denominator of the first fraction is larger, 3/4 is greater than 3/8.
So, it is not enough to consider only the denominators when comparing fractions with the same numerator; instead, you need to compare how the denominators relate to each other in order to determine which fraction is greater.